What is a general solution to the differential equation #dy/dx=(2x)/(y+x^2y)^2#?

Question

8606 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-09T23:09:23

#y = root3( C - 3/(1+x^2)) #

#dy/dx=(2x)/(y+x^2y)^2#

this is separable

#dy/dx=1/y^2 * (2x)/(1+x^2)^2#

#y^2 dy/dx= (2x)/(1+x^2)^2#

#implies y^3/3 = - 1/(1+x^2) + C#

#y^3 = C - 3/(1+x^2) #

#y = root3( C - 3/(1+x^2)) #